CN108388229A - The random hybrid system health evaluating method of quadrotor based on health degree - Google Patents

Abstract

The invention discloses a health assessment method for a four-rotor random hybrid system based on health, and belongs to the technical field of aircraft health management. The present invention first establishes a four-rotor random hybrid system model. The discrete mode of the model considers the sensor health mode and different types of sensor anomaly models; the continuous dynamic behavior of each mode is described by the process equation and the measurement equation, where the process equation uses the augmented variable method to model the actuator performance. Efficiency, measurement equations in different modalities model the observed behavior of different types of sensor anomalies. Then, the hybrid state evaluation of the quadrotor is realized by using the improved interactive multi-model algorithm. Finally, a health index is proposed for quantitative health assessment of quadrotors. The invention can solve the problem that it is difficult to quantitatively measure the dynamic performance of the system during the four-rotor flight process, and can also effectively identify the situation that the actuator and the sensor fail at the same time.

Description

Health assessment method for quadrotor stochastic hybrid system based on health degree

technical field

The invention relates to a health assessment method for a four-rotor random hybrid system based on health, and belongs to the technical field of aircraft health management.

Background technique

Quadrotor aircraft (hereinafter referred to as quadrotor), as a vertical take-off and landing unmanned aerial vehicle, has been used in many military and civilian mission scenarios such as real-time monitoring, search and rescue, pipeline/power inspection, environmental monitoring, and agricultural plant protection. From the perspective of reliability, it is difficult to guarantee that the quadrotor will not have software and hardware failures or abnormal performance in various aspects including communications, sensors, power systems, and fuselage structures during flight. These failures and abnormalities may lead to mission interruption, crash, and even threaten the lives and property safety of ground personnel. In recent years, with the promotion of quadrotor application scope, the expansion of market scale and the increase of the number of individual users, it is of great theoretical significance and engineering value to study the reliability of quadrotor flight.

System health management technology uses system models, observation data and related algorithms to detect process abnormalities, evaluate health degradation, predict remaining life, and then formulate corresponding maintenance and operation strategies to ensure that the system completes the expected functions. Under the technical framework of health management, health assessment analyzes the system observation data and combines the system model to evaluate whether the current working state of the system is normal, and whether the system has potential health degradation in a certain period of time in the future. The airborne systems of large foreign aircraft are equipped with advanced health management systems to achieve highly reliable flight and healthy service. However, most of the solutions to quadrotor flight reliability problems are based on fault diagnosis and fault-tolerant control. There are few studies on using "health" to measure the overall performance of quadrotors, and exploring how to ensure reliable flight of quadrotors based on this. This is mainly due to the unclear definition of the health of dynamic systems such as quadrotors and the lack of reasonable metrics. Most existing health management research usually uses "fault" and "lifetime" to describe "health".

Contents of the invention

The purpose of the present invention is to solve the above problems, make up for the shortcomings in the research on the reliability of quadrotor flight, and take "health" as the guide, propose a health assessment method for quadrotor random hybrid system based on health, in order to solve the problem of quadrotor flight Reliability issues provide a new way of thinking and feasible solutions.

The present invention provides a health assessment method based on the health degree of a four-rotor random hybrid system. The specific steps of the method are as follows:

Step 1: Establish a quadrotor random hybrid system model.

Establish the quadrotor dynamic model process equations, including kinematic equations, dynamic equations and control distribution equations. The input of the kinematic equation is linear velocity and angular velocity, and the output is position and attitude; the input of the dynamic equation is force and moment (thrust, pitch moment, roll moment, and yaw moment), and the output is the speed and angular velocity of the quadrotor; The governing distribution equation distributes the forces and moments to the four paddles. An efficiency coefficient matrix is introduced into the control assignment model to model actuator failures such as actuator efficiency degradation.

Discrete modes are defined according to different types of sensor anomalies. The continuous dynamic behavior of each mode is described by process equations and measurement equations. The measurement equations in different modes reflect the observed behavior of different types of sensor anomalies. The discrete modes are switched according to the probability, and the continuous dynamic behavior of each mode is combined to form the quadrotor stochastic hybrid system model.

Step 2: Quadrotor hybrid state estimation.

The interactive multi-model algorithm is a filter-based recursive estimator that can efficiently estimate the hybrid state distribution of stochastic hybrid systems. There are two deficiencies in the direct application of the classic interactive multi-model algorithm to system state estimation. First, the modal transition probabilities of the classical interactive multi-model algorithm remain constant during the state estimation process, which can lead to false modal identifications; second, the "interaction" step of the classical interactive multi-model algorithm can make the estimator covariance The matrix recurses in a non-Gaussian manner, resulting in a mixed state distribution that cannot be used for health calculations. Therefore, based on the quadrotor stochastic hybrid system model, the improved interactive multi-model algorithm is used to estimate the quadrotor hybrid state distribution, including the probability density function of the process variable and the discrete probability distribution of the discrete mode.

Step 3: Actuator Efficiency Coefficient Calculation and Sensor Abnormal Type Identification

Combined with the quadrotor random hybrid system model, the efficiency coefficient of the actuator is calculated by using the hybrid state distribution of the quadrotor obtained by the improved interactive multi-model algorithm, and the abnormal type of the sensor is identified.

Step 4: Calculation of quadrotor health

Industrial system health metrics are quantitative indicators that measure the overall working status or performance of the system. Process variables are directly used as indicators to evaluate the dynamic performance of the system. The results are easily affected by external noise, resulting in inaccurate evaluation. Therefore, a health index is proposed to quantitatively evaluate the health of the quadrotor, which can more comprehensively evaluate the dynamic performance of the quadrotor.

The advantages of the present invention are:

(1) The present invention models the quadrotor as a stochastic hybrid system, considers different types of potential anomalies, and considers the continuous dynamic behavior of the quadrotor and the uncertainty of abnormal occurrence, improving the applicability and accuracy of health assessment;

(2) The present invention utilizes the improved interactive multi-model algorithm to estimate the distribution of the mixed state of the quadrotor, not only the probability density function of the process variable of the quadrotor can be estimated, but also the discrete probability distribution of the discrete mode can be estimated, which can effectively deal with actuators and sensors at the same time failure scenarios;

(3) The present invention proposes a health index to measure the health of the quadrotor, which solves the problem that the health of the quadrotor is difficult to measure quantitatively during the flight process, and improves the accuracy of health assessment compared with the process variable as a measurement index.

Description of drawings

Fig. 1 is a flowchart of a health assessment method for a quadrotor random hybrid system based on health.

Figure 2 is a schematic diagram of a "+" quadrotor.

Fig. 3 is an example diagram of the structure of the four-rotor random hybrid system of the present invention.

Fig. 4 is a schematic diagram of the improved interactive multi-model algorithm of the present invention.

Fig. 5 is a schematic diagram of a quadrotor healthy space according to the present invention.

Fig. 6 is a diagram of calculation results of actuator efficiency coefficients obtained based on the improved interactive multi-model algorithm in the present invention.

Fig. 7 is a diagram of the identification results of sensor anomalies obtained based on the improved interactive multi-model algorithm of the present invention.

Fig. 8 is a diagram of the calculation result of the health degree of the present invention.

Detailed ways

The present invention will be further described in detail with reference to the accompanying drawings and embodiments.

The invention is a health assessment method for a four-rotor random hybrid system based on the health degree. Firstly, a four-rotor random hybrid system model is established. The discrete mode of the model considers the health status of the sensor and the abnormal status of different types of sensors; the continuous dynamic behavior of each mode is described by the process equation and the measurement equation, in which the process equation uses the augmented variable method to model the execution efficiency of the actuator , the measurement equations in different modalities model the observed behavior of different types of sensors when they are anomalous. Then, the hybrid state estimation of the quadrotor is realized by using the improved interactive multi-model algorithm. Finally, a health index is proposed to quantitatively evaluate the health of the quadrotor, which can also effectively identify the situation where actuators and sensors fail at the same time.

The present invention is a health assessment method based on the health degree of a four-rotor random hybrid system. The specific implementation process is shown in Figure 1, and it is realized through the following steps:

Step 1: Establish a quadrotor random hybrid system model.

The process equation of establishing the quadrotor dynamic model is as follows:

In the formula, Indicates the position of the quadrotor in the ground coordinate system;

Indicates the speed of the quadrotor in the ground coordinate system; Indicates the attitude angle of the quadrotor; Indicates the rotational angular rate of the quadrotor around the body axis; Indicates the total pulling force produced by the propeller; Indicates the torque generated by the propeller tension on the body axis; m is the mass of the quadrotor; g is the acceleration due to gravity; Indicates the moment of inertia of the quadrotor. Let { ^e p _x,d , ^e p _y,d , ^e p _z,d ,φ _d ,θ _d ,ψ _d } denote the desired quadrotor position and attitude. Design the PD controller as follows:

and

In the formula, is the virtual control quantity, the parameter are the control parameters corresponding to each control quantity of the PD controller. For the "+" quadrotor shown in Fig. 2, the control allocation model can be expressed as follows

In the formula, Indicates the lift generated by the four propellers; H represents the control distribution matrix; d represents the distance between the rotor and the center of the body; λ _i , i=1, 2, 3, 4 represents the ratio of each propeller torque to lift.

Introduce efficiency matrix

Λ=diag(η ₁ η ₂ η ₃ η ₄ ) (5)

In the formula, η _i ∈ [0,1], i = 1, 2, 3, 4 represent the execution efficiency of the i-th actuator, η _i = 1 means that the i-th actuator is completely healthy and works normally, η _i = 0 means that the i-th actuator fails completely, and η _i ∈ (0,1) reflects the partial degradation of the i-th actuator's efficiency. Quadrotor actuator efficiency anomalies can be modeled as

Suppose x＝[ ^e p _x ^e p _y ^e p _z ^e v _x ^e v _y ^e v _z φ θ ψ ^b ω _x ^b ω _y ^b ω _z ] ^T is the quadrotor process variable, then the observation equation is

y=Cx+Γ _v v (7)

In the formula, y represents the observation quantity of the quadrotor; C represents the observation matrix; v represents the observation noise of the quadrotor, and Γ _v is the noise driving array. The modeling of sensor abnormal behavior is achieved by changing the observation matrix C and the noise term _Γvv .

Assume

In the formula, q _j is the discrete mode of the quadrotor, which represents different health levels, such as full health mode, GPS abnormal mode, barometer abnormal mode, etc., and M is the number of modes. The switching between modes is described by a Markov chain, that is,

In the formula, k is the sampling time; p _j is the probability that the quadrotor is in mode q _j , satisfying π _ij is the mode switching probability, satisfying

for Both have discrete-time continuous (variable) dynamic behavior:

In the formula, F _j (x(k-1), u(k-1), Λ(k-1)) can be discretized in time by formulas (1)-(5); is the Gaussian process noise, is the noise driver, is the noise covariance matrix; the measurement noise term is the noise driver, is the noise covariance matrix. So far, the quadrotor stochastic hybrid system model has been established. Taking M=3 as an example, the structure diagram of the four-rotor random hybrid system model is shown in Figure 3.

Step 2: Quadrotor hybrid state estimation.

Given the moment k=0, the initial hybrid state distribution of the quadrotor is

In the formula, f(x(0)|q _j (0)) represents the probability density function of the process variable x(0) when the quadrotor is in mode q _j at time k=0, x _j (0),P _j (0) is the mean value and covariance matrix of the initial normal distribution, and p _j (0) represents the probability that the quadrotor is in mode q _j at k=0.

Assuming the current time is k, let Y ^k ={y(0),y(1),...,y(k)} represent the observations at the system cut-off time k. On the basis of the classic interactive multi-model algorithm, using the improved interactive multi-model algorithm to realize hybrid state estimation mainly includes five steps:

1) Estimator interaction

For j=1,2,...,M

Predicted modal probabilities:

Interaction Modality Probability:

Interactive system process variables:

In the formula, E represents the mathematical expectation operator, Represents the estimator of the process variable x. Cancel the covariance matrix interaction and assign only the covariance matrix:

2) Parallel filtering

For j=1,2,...,M

Forecast status:

Compute the Jacobian matrix:

Prediction covariance matrix

In the formula, cov represents the covariance matrix operator.

Compute the measurement residuals:

Compute the measurement residual covariance matrix:

Compute the Kalman gain:

Update process variables:

Update the covariance matrix:

In the formula, I represents the identity matrix.

3) Update modal probability and modal identification

For j=1,2,...,M

Compute the likelihood function:

In the formula, exp represents the exponential operator.

Update the modal probabilities:

Modal recognition:

In the formula, p _T represents the probability threshold.

4) Estimator Fusion

Process variable fusion:

Covariance matrix fusion:

5) Transition probability matrix update

Assume that the system is in mode q _i at time k-1, and mode q _j at time k, and q _i ≠ q _j . Let elementary matrix

Then the transition probability matrix Π(k) is updated according to the following formula:

Π(k)=Ξ Π(k-1) Ξ (30)

The schematic diagram of the improved interactive multi-model algorithm is shown in Figure 4. Based on this algorithm, the real-time hybrid state distribution of the quadrotor can be obtained: including the discrete mode probability and the probability density function of the continuous state variable under each model

Step 3: Calculate the efficiency coefficient of the actuator and identify the abnormal type of the sensor.

According to formula (6), for Have

In the formula, is the residual error of the input quantity in the q _j mode, which can be estimated by the improved interactive multi-model algorithm by means of augmented variables. Combined formula (5), there are

In the formula, [] _i represents the i-th component of the vector; denote the estimated value of the i-th actuator efficiency in the q _j mode, represents the estimated value of the i-th actuator efficiency considering all modal situations comprehensively.

Based on the modal identification step of the improved interactive multi-model algorithm, the sensor anomaly type identification can be realized.

Step 4: Calculation of quadrotor health.

For a dynamic system, assume that the n-dimensional space where its state variable x resides Can be divided into a healthy space S _H and an unhealthy space For a certain time k, the health of the system is

Equation (34) can be interpreted as the health value of the dynamic system at time k is the probability that the system stays in the healthy space at this time.

For a quadrotor, the healthy space during its flight can be understood as the "healthy flight envelope" of the quadrotor, as shown in Figure 5. Considering that the quadrotor may be in any working mode during flight, and the waypoint changes with time, the health of the quadrotor is

The calculation method is as follows:

Example 1:

Step 1: Establish a quadrotor random hybrid system model.

Consider three scenarios: actuator efficiency anomaly, GPS anomaly and barometer anomaly. Therefore, to define the system mode of the quadrotor q ₁ indicates the sensor healthy mode, q ₂ indicates the GPS abnormal mode, and q ₃ indicates the barometer abnormal mode. The dynamic model of the quadrotor in each mode has process equations and measurement equations. For the process equation, all modes are the same, which can be obtained from formula (10), namely

F ₁ =F ₂ =F ₃ =F

Γ _w,1 = Γ _w,2 = Γ _w,3 = Γ _w (37)

Qw _,1 =Qw _,2 =Qw _,3 = _Qw

Each mode of the quadrotor corresponds to a different measurement equation. In the sensor health mode, it is considered that the 12 process variables of the quadrotor can be directly measured, that is, if C=I ₁₂ , then y=x+Γ _v v; in the GPS abnormal mode, it is considered that the measured { ^e p _x , ^e p _y } are unreliable, the measurement equation needs to delete the first two lines, that is, the unreliable measured value of { ^e p _x , ^e p _y } should not be used for state estimation; in the abnormal mode of the barometer, it is considered that the measurement The obtained ^e p _z is unreliable, and its measurement equation needs to delete the third line, that is, the unreliable measured value of ^e p _z should not be used for state estimation. Based on this, the mode switching probability is set as

The parameters of the quadrotor dynamic model are shown in Table 1.

Table 1 Quadrotor dynamic model parameters

Step 2: Quadrotor hybrid state estimation.

As shown in Table 2, the quadrotor flight mission route is set, and the mixed state distribution of the quadrotor is estimated according to equations (12)-(30).

Table 2 Quadrotor mission route

Step 3: Calculate the efficiency coefficient of the actuator and identify the abnormal type of the sensor.

Combined with the quadrotor random hybrid system model, the efficiency coefficient of the actuator can be calculated by using the hybrid state distribution of the quadrotor obtained by the improved interactive multi-model algorithm, as shown in Figure 6. The time period for the system abnormality to occur is shown in Table 3, taking p _T =0.8, the type of sensor abnormality can be identified, as shown in Figure 7 . The results show that the actuator efficiency coefficient can be effectively estimated and the sensor anomaly types can be correctly identified.

Step 4: Calculation of quadrotor health.

The quadrotor health is calculated according to formula (36), and the results are shown in Figure 8, which shows that the health can effectively reflect the health degradation of the quadrotor and the impact of abnormalities on the entire quadrotor flight.

Claims (5)

1. A method for evaluating the health of a four-rotor random hybrid system based on the degree of health, characterized in that the specific steps of the method are as follows: Step 1: Establish a quadrotor random hybrid system model; Establish the quadrotor dynamic model process equations, including kinematic equations, dynamic equations and control distribution equations. The input of the kinematic equation is linear velocity and angular velocity, and the output is position and attitude; the input of the dynamic equation is force and moment, and the output is The speed and angular velocity of the quadrotor; the control distribution equation distributes the force and moment to the four propellers; the efficiency coefficient matrix is introduced in the control distribution model to model actuator efficiency degradation and actuator failure; Discrete modes are defined according to different sensor anomalies. The continuous dynamic behavior of each mode is described by process equations and measurement equations. The discrete modes are switched according to probability. Combined with the continuous dynamic behavior of each mode, a quadrotor random hybrid system model is formed. ; Step 2: Estimation of the hybrid state of the quadrotor; Therefore, based on the quadrotor stochastic hybrid system model, the improved interactive multi-model algorithm is used to estimate the quadrotor hybrid state distribution, including the probability density function of the process variable and the discrete probability distribution of the discrete mode; Step 3: Calculate the efficiency coefficient of the actuator and identify the abnormal type of the sensor; Combined with the quadrotor random hybrid system model, using the quadrotor hybrid state distribution obtained by the improved interactive multi-model algorithm, calculate the actuator efficiency coefficient, and identify the abnormal type of the sensor; Step 4: Calculate the quadrotor health. 2. A health-based four-rotor random hybrid system health assessment method according to claim 1, wherein said step one is specifically: The process equation of establishing the quadrotor dynamic model is as follows: In the formula, Indicates the position of the quadrotor in the ground coordinate system; Indicates the speed of the quadrotor in the ground coordinate system; Indicates the attitude angle of the quadrotor; Indicates the rotational angular rate of the quadrotor around the body axis; Indicates the total pulling force produced by the propeller; Indicates the torque generated by the propeller tension on the body axis; m is the mass of the quadrotor; g is the acceleration due to gravity; Represents the moment of inertia of the quadrotor; let { ^e p _x,d , ^e p _y,d , ^e p _z,d ,φ _d ,θ _d ,ψ _d } represent the desired position and attitude of the quadrotor; design the PD controller as follows : and In the formula, is the virtual control quantity, the parameter are the control parameters corresponding to each control quantity of the PD controller, and for the "+" type quadrotor, the control allocation model is: In the formula, Indicates the lift generated by the four propellers; H represents the control distribution matrix; d represents the distance between the rotor and the center of the body; λ _i , i=1, 2, 3, 4 represents the ratio of the torque to the lift of each propeller; Introduce efficiency matrix Λ=diag(η ₁ η ₂ η ₃ η ₄ ) (5) In the formula, η _i ∈ [0,1], i = 1, 2, 3, 4 represent the execution efficiency of the i-th actuator, η _i = 1 means that the i-th actuator is completely healthy and works normally, η _i = 0 means that the i-th actuator fails completely, and η _i ∈ (0,1) reflects the partial degradation of the i-th actuator's efficiency; the quadrotor actuator efficiency anomaly is modeled as Suppose x＝[ ^e p _x ^e p _y ^e p _z ^e v _x ^e v _y ^e v _z φ θ ψ ^b ω _x ^b ω _y ^b ω _z ] ^T is the quadrotor process variable, then the observation equation is y=Cx+Γ _v v (7) In the formula, y represents the observation quantity of the quadrotor; C represents the observation matrix; v represents the observation noise of the quadrotor, and Γ _v is the noise driving array; the modeling of the abnormal behavior of the sensor is realized by changing the observation matrix C and the noise term Γ _v v; Assume In the formula, q _j is the discrete mode of the quadrotor, representing different health levels, M is the number of modes; the switching between modes is described by the Markov chain, that is, In the formula, k is the sampling time; p _j is the probability that the quadrotor is in mode q _j , satisfying π _ij is the mode switching probability, satisfying for Both have discrete-time continuous dynamic behavior: In the formula, F _j (x(k-1), u(k-1), Λ(k-1)) is obtained by discretizing formulas (1)-(5) in time; is the Gaussian process noise, is the noise driver, is the noise covariance matrix; the measurement noise term is the noise driver, is the noise covariance matrix, and finally, the quadrotor random hybrid system model is obtained. 3. A health-based four-rotor random hybrid system health assessment method according to claim 1, characterized in that, the second step is specifically: Given the moment k=0, the initial hybrid state distribution of the quadrotor is In the formula, f(x(0)|q _j (0)) represents the probability density function of the process variable x(0) when the quadrotor is in mode q _j at time k=0, x _j (0),P _j (0) is the mean value and covariance matrix of the initial normal distribution, p _j (0) represents the probability that the quadrotor is in mode q _j at k=0; Assuming the current moment is k, let Y ^k ={y(0),y(1),...,y(k)} represent the observed quantity of the system at the cut-off time k, and use the improved interactive multi-model algorithm to realize the hybrid state estimation including: 1) Estimator interaction For j=1,2,...,M Predicted modal probabilities: Interaction Modality Probability: Interactive system process variables: In the formula, E represents the mathematical expectation operator, Represents the estimator of the process variable x; Cancel the covariance matrix interaction and assign only the covariance matrix: 2) Parallel filtering For j=1,2,...,M Forecast status: Compute the Jacobian matrix: Prediction covariance matrix In the formula, cov represents the covariance matrix operator; Compute the measurement residuals: Compute the measurement residual covariance matrix: Compute the Kalman gain: Update process variables: Update the covariance matrix: In the formula, I represents the identity matrix; 3) Update modal probability and modal identification For j=1,2,...,M Compute the likelihood function: In the formula, exp represents the exponential operator; Update the modal probabilities: Modal recognition: In the formula, p _T represents the probability threshold; 4) Estimator Fusion Process variable fusion: Covariance matrix fusion: 5) Transition probability matrix update Assume that the system is in q _i mode at time k-1, and in q _j mode at time k, and q _i ≠ q _j ; let the elementary matrix Then the transition probability matrix Π(k) is updated as: Π(k)=Ξ Π(k-1) Ξ (30) Obtaining real-time hybrid state distributions for quadrotors: including discrete mode probabilities and the probability density function of the continuous state variable under each model 4. A health-based four-rotor random hybrid system health assessment method according to claim 1, characterized in that said step three is specifically: for Have In the formula, is the input volume residual in q _j mode, then In the formula, [] _i represents the i-th component of the vector; denote the estimated value of the i-th actuator efficiency in the q _j mode, represents the estimated value of the i-th actuator efficiency considering all modal situations comprehensively. 5. A health-based four-rotor random hybrid system health assessment method according to claim 1, characterized in that said step four is specifically: For a dynamic system, assume that the n-dimensional space where its state variable x resides Divided into a healthy space _SH and an unhealthy space S _F , For a certain time k, the health of the system is Equation (34) explains that the health value of the dynamic system at time k is the probability that the system stays in the healthy space at that time; For a quadrotor, the healthy space during its flight is understood as the "healthy flight envelope" of the quadrotor, and the health of the quadrotor is The calculation method is as follows: